PRICING SUPPLEMENT NO. 33                                         Rule 424(b)(3)
DATED: September 1, 2004                                     File No. 333-109793
(To Prospectus dated November 17, 2003,
and Prospectus Supplement dated November 17, 2003)

                                 $10,668,950,162
                         THE BEAR STEARNS COMPANIES INC.
                           Medium-Term Notes, Series B

Principal Amount: $5,000,000     Floating Rate Notes [x]  Book Entry Notes [x]

Original Issue Date: 9/24/2004   Fixed Rate Notes [ ]     Certificated Notes [ ]

Maturity Date:  9/24/2009        CUSIP#: 073928G72

Option to Extend Maturity:       No    [x]
                                 Yes   [ ]    Final Maturity Date:

Minimum Denominations: $100,000, increased in multiples of $10,000

                                             Optional          Optional
                         Redemption         Repayment         Repayment
   Redeemable On          Price(s)           Date(s)           Price(s)
   -------------         ----------         ---------         ---------
        N/A                 N/A                N/A               N/A

Applicable Only to Fixed Rate Notes:
-----------------------------------

Interest Rate:

Interest Payment Dates:

Applicable Only to Floating Rate Notes:
--------------------------------------

Interest Rate Basis:                         Maximum Interest Rate:  N/A

[ ]  Commercial Paper Rate                   Minimum Interest Rate:  N/A

[ ]  Federal Funds Effective Rate

[ ]  Federal Funds Open Rate                 Interest Reset Date(s):  *

[ ]  Treasury Rate                           Interest Reset Period:  Monthly

[ ]  LIBOR Reuters                           Interest Payment Date(s):  **

[ ]  LIBOR Telerate                          Interest Determination Date(s): ***

[ ]  Prime Rate

[x]  CMT Rate+                               Multiplier: 0.715

Initial Interest Rate: [TBD]%                Interest Payment Period:  Monthly

Index Maturity:  Ten Years

Spread (plus or minus): N/A

* On the 24th of each month prior to Maturity.

** On the 24th of each month, including the maturity date.

*** On the second Business Day prior to each Interest Reset Date.



+     The Interest Rate for each Interest Payment Period shall be determined by
      the Calculation Agent in accordance with the following formula:

                        (10 Year CMT Rate) x (Multiplier)

                 Where:

                 10 Year CMT Rate = the 10 Year CMT Rate displayed on CMT
                 Telerate page 7051

                 Multiplier = 0.715

The distribution of Notes will conform to the requirements set forth in Rule
2720 of the NASD Conduct Rules.


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